Line dinner plates or wide bowls equally with whole lettuce leaves, then Belgian endive leaves.
In a large bowl, combine shredded lettuce and parsley. Add 2/3 cup deviled Louis dressing and mix gently. Divide equally among lettuce-lined plates.
Remove and discard any bits of shell from crab. Mound crab in center of shredded lettuce mixture; arrange tomato and egg wedges around edges. Sprinkle salads with chopped chives and garnish with whole chives. Offer remaining dressing, salt and pepper, and lemon wedges to season salads to taste.